CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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From: |-|ercules on 27 Jun 2010 04:29 "Sylvia Else" <sylvia(a)not.here.invalid> wrote > On 27/06/2010 4:34 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>> If you think my induction only works on finite prefixes and not over >>>> entire infinite expansions >>>> then YOU prove that assertion. >>>> >>> >>> Consider the following proposition: >>> >>> For any *finite* list of infinite digit sequences, one can use the >>> anti-diagonal method to produce a sequence that is not in the list. >>> >>> Do you have any difficulty with that? >> >> No. This is precisely my point. >> >> 123 >> 456 >> 789 >> >> Diag = 159 >> Anti-Diag = 260 >> >> 260 is a NEW DIGIT SEQUENCE. >> > > OK, so you accept that it is true for any finite list. That is, that for > any finite list there is a sequence that is not in the list, or to put > it another way, all finite lists omit at least one sequence. YES YES YES I AGREE THERE!!!! Good proof you have of that! > Note that the requirement that the length of the list be finite doesn't > impose any maximum on the length. > > By analogy with your argument that extrapolates from a list that > contains all finite permutations to a list that contains all infinite > sequences, I'll argue that by extroplating from the fact that all finite > lists omit at least one sequence one can conclude that an infinite list > omits at least one sequence. > > The latter of course contradicts your thesis, but either extrapolating > from the finite to the infinite is valid, or it isn't. Without some > demonstration that the circumstances are materially different, you can't > argue that the extrapolation is valid in one case, and invalid in the other. > > Sylvia. Rather than point out differences, let's agree one must be careful extrapolating to infinity, then note your proof makes a claim about infinity, my proof makes a more conservative statement not to draw conclusions. Herc
From: Sylvia Else on 27 Jun 2010 04:52 On 27/06/2010 6:29 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote >> On 27/06/2010 4:34 PM, |-|ercules wrote: >>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>>> If you think my induction only works on finite prefixes and not over >>>>> entire infinite expansions >>>>> then YOU prove that assertion. >>>>> >>>> >>>> Consider the following proposition: >>>> >>>> For any *finite* list of infinite digit sequences, one can use the >>>> anti-diagonal method to produce a sequence that is not in the list. >>>> >>>> Do you have any difficulty with that? >>> >>> No. This is precisely my point. >>> >>> 123 >>> 456 >>> 789 >>> >>> Diag = 159 >>> Anti-Diag = 260 >>> >>> 260 is a NEW DIGIT SEQUENCE. >>> >> >> OK, so you accept that it is true for any finite list. That is, that >> for any finite list there is a sequence that is not in the list, or to >> put it another way, all finite lists omit at least one sequence. > > > YES YES YES I AGREE THERE!!!! > Good proof you have of that! > > > >> Note that the requirement that the length of the list be finite >> doesn't impose any maximum on the length. >> >> By analogy with your argument that extrapolates from a list that >> contains all finite permutations to a list that contains all infinite >> sequences, I'll argue that by extroplating from the fact that all >> finite lists omit at least one sequence one can conclude that an >> infinite list omits at least one sequence. >> >> The latter of course contradicts your thesis, but either extrapolating >> from the finite to the infinite is valid, or it isn't. Without some >> demonstration that the circumstances are materially different, you >> can't argue that the extrapolation is valid in one case, and invalid >> in the other. >> >> Sylvia. > > Rather than point out differences, let's agree one must be careful > extrapolating to infinity, > then note your proof makes a claim about infinity, my proof makes a more > conservative statement > not to draw conclusions. You purport to extrapolate from all finite permutations to all infinite sequences. In the process you also move from a list of finite length to an infinite one (since otherwise it cannot contain infinitely many sequences). There doesn't seem anything conservative about that. But why not point out the *material* differences? Also, since you agree one must be careful extrapolating to infinity, you'd have to agree that any such extrapolation must be carefully justified, not just have its truth vaguely asserted, with the odd choice insult thrown in the direction of anyone who's sceptical. Sylvia.
From: |-|ercules on 27 Jun 2010 05:27 "Sylvia Else" <sylvia(a)not.here.invalid> wrote > On 27/06/2010 6:29 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>> On 27/06/2010 4:34 PM, |-|ercules wrote: >>>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>>>> If you think my induction only works on finite prefixes and not over >>>>>> entire infinite expansions >>>>>> then YOU prove that assertion. >>>>>> >>>>> >>>>> Consider the following proposition: >>>>> >>>>> For any *finite* list of infinite digit sequences, one can use the >>>>> anti-diagonal method to produce a sequence that is not in the list. >>>>> >>>>> Do you have any difficulty with that? >>>> >>>> No. This is precisely my point. >>>> >>>> 123 >>>> 456 >>>> 789 >>>> >>>> Diag = 159 >>>> Anti-Diag = 260 >>>> >>>> 260 is a NEW DIGIT SEQUENCE. >>>> >>> >>> OK, so you accept that it is true for any finite list. That is, that >>> for any finite list there is a sequence that is not in the list, or to >>> put it another way, all finite lists omit at least one sequence. >> >> >> YES YES YES I AGREE THERE!!!! >> Good proof you have of that! >> >> >> >>> Note that the requirement that the length of the list be finite >>> doesn't impose any maximum on the length. >>> >>> By analogy with your argument that extrapolates from a list that >>> contains all finite permutations to a list that contains all infinite >>> sequences, I'll argue that by extroplating from the fact that all >>> finite lists omit at least one sequence one can conclude that an >>> infinite list omits at least one sequence. >>> >>> The latter of course contradicts your thesis, but either extrapolating >>> from the finite to the infinite is valid, or it isn't. Without some >>> demonstration that the circumstances are materially different, you >>> can't argue that the extrapolation is valid in one case, and invalid >>> in the other. >>> >>> Sylvia. >> >> Rather than point out differences, let's agree one must be careful >> extrapolating to infinity, >> then note your proof makes a claim about infinity, my proof makes a more >> conservative statement >> not to draw conclusions. > > You purport to extrapolate from all finite permutations to all infinite > sequences. In the process you also move from a list of finite length to > an infinite one (since otherwise it cannot contain infinitely many > sequences). There doesn't seem anything conservative about that. > > But why not point out the *material* differences? You won't follow them. Every time I say induction you'll say finite prefix. > > Also, since you agree one must be careful extrapolating to infinity, > you'd have to agree that any such extrapolation must be carefully > justified, not just have its truth vaguely asserted, with the odd choice > insult thrown in the direction of anyone who's sceptical. > > Sylvia. You claim transfinite sets based on a missing box of missing box numbers. I'm just calling your bullshit. Herc
From: |-|ercules on 27 Jun 2010 08:44 "Sylvia Else" <sylvia(a)not.here.invalid> wrote > > You purport to extrapolate from all finite permutations to all infinite > sequences. The difference is I'm using finite prefix permutations. What would be good is an axiom or theorem to assert All finite prefix sequences + no constraint on the suffix -> all infinite sequences Herc
From: Jim Burns on 27 Jun 2010 09:57
George Greene wrote: > On Jun 26, 6:05 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> It is perplexing if outputs of all computer programs are listed, >> how do you find a program to compute the diagonal digit >> at the position that is contradictory? > > You just write the program that says output(n) = 9 - L(n,n) > AND YOU'RE DONE, VOILA, > WHOOT, THERE IT IS! > It is a VERY SIMPLE program. > But there is no "contradictory" position. > The number being computed simply IS NOT ON the list. Consider the list L (which is in no way an attempt to list all the reals), .4999... .0900... .00900... ... that is, L(n) = { .499... , n = 1 { 9/10^n , otherwise Your program produces output = .5000... However, .5000... = .4999... so the proposed anti-diagonal /is/ on this list. The problem is not with Cantor's argument, it is with your 9 - L(n,n). Use a better digit-selecting function and it goes away. Jim Burns |